infinity plus anything = infinity. it's not a higher or lower infinity. its the same infinity. because either way its going on forever no matter how much you take away or add or divide by... unless you divide infinity by infinity. that's 1. or divide infinity by 0, can't be done. or subtract infinity from infinity, that's 0.

very good...that's why this is a theoretical question and answer. lyou can't actually have an infinite number of zeros lined up, so you can't have a one at the end. but in theory, it is possible to say that after the infinte number of zeros, there will be a one, much like saying that after the infinite number of reals following 1, there is a 2. slightly different circumstance, but similar enough.

But on the 1 and 2...

You are giving "restrictions" to your set of infinity...

You are saying "between" 1 and 2 ONLY....So the infinity between 1 and 2 yes you can...

But this infinity, (and all others where you don't add "restrictions") numbers don't go on the end...

There are numbers after the infinity between 1 and 2...But there aren't after infinity...

infinity plus anything = infinity. it's not a higher or lower infinity. its the same infinity. because either way its going on forever no matter how much you take away or add or divide by... unless you divide infinity by infinity. that's 1. or divide infinity by 0, can't be done. or subtract infinity from infinity, that's 0.

This is debated all the time, and really can't be answered.

If you have a full sandwich, eat one half of it, eat another half, eat another half.

Keep eating it in half, will the sandwich ever be finished?

Mathematically no, engineers would usually say yes.

What is this, the gourmand's version of Xeno's paradox?

The "problem" is actually similar to those encountered in asymptotic calculus, but in practice it's clearly a simple one to solve. Look to the philosophy of Democritus for an answer.

.333 repeating forever is just the numerical representation. it will never actually be equal to the true value of 1/3... it will keep on going forever and never actually approach the true value of 1/3. .333 is approaching the asymptote of 1/3 but never actually touches it just like .999 repeating does 1.

Quote:

And what is 1 - 0.9 repeat

a number that gets closer and closer to the asymptote of 0 as can be done as the decimals go on without actually touching it.

Well the smallest piece of matter as we take it is the atom, so you would split it up to the last atom, then you would split the last atom of the sandwich and then blow up.

usually when given a particular complex function you need to integrate and you cant, you need to rely on integration by parts. eventually you will get a product minus an integral with an easily antidifferentiable function.

however, sometimes there is a phenomenon when if you continue to integrate by parts, the original integral appears again as you integrate. durin these circumstances, you can create a reduction formula in which you can easily calculate the integral of any family of functions which share a common attribute:

.333 repeating forever is just the numerical representation. it will never actually be equal to the true value of 1/3... it will keep on going forever and never actually approach the true value of 1/3. .333 is approaching the asymptote of 1/3 but never actually touches it just like .999 repeating does 1.

So then what is the true value of 1/3 that 0.33 repeating keeps approaching?
There is no answer to that from you, because
0.3 repeating IS the true value of 1/3

Once again, do you know how to divide numbers like that on paper? Like 3/5, do you know how to do that on paper? It will give you 0.6...Now, do 1/3 on paper, and suprise, 0.33 will start coming up, forever...

Quote:

a number that gets closer and closer to the asymptote of 0 as can be done as the decimals go on without actually touching it.

That makes no sense at all...

Your acting like 0 is the only number it can't equal...So can it equal 0.2?

I've been thining about this for awhile. Check it out.

1/9 is .1 repeating
2/9 is .2 repeating
3/9 is .3 repeating and also 1/3
.
.
etc
.
.
so, 9/9 is .9 repeating... and also from fractions we know that to be 1.